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Exact Solutions and Conservation Laws of the Joseph-Egri Equation with Power Law Nonlinearity Read chapter Read first chapter

2015 | OriginalPaper | Chapter

A Free Boundary Approach to Solve the Equilibrium Equations of a Membrane

Authors : Giuseppe Viglialoro, Álvaro González, Juan Murcia

Published in: Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Publisher: Springer International Publishing

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Abstract

This chapter deals with a mathematical problem related to the equilibrium analysis of a membrane with rigid and cable boundary. The membrane and its boundary are respectively identified with a regular surface and a set of regular curves. The equilibrium is directly expressed by means of an elliptic problem, in terms of the shape of the membrane and its stress tensor; therefore, a free boundary numerical resolution procedure is presented and applied in a particular case.

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Footnotes
1
If \(f(x,y)\) is a function, we will write \(f_{,x}=\dfrac{\partial f}{\partial x},\;f_{,y}=\dfrac{\partial f}{\partial y},\,f_{,xx}=\dfrac{\partial^2 f}{\partial x^2}\,\;\text{and so on}.\)
 
Literature
1.
Crank, J.: Free and Moving Boundary Problems, Oxford University Press, New York (1984)MATH
2.
Murcia, J.: Structural membrane technology for footbridges. Inf. Constr. 59(507), 21–31 (2007)
3.
Viglialoro, G., Murcia, J.: Equilibrium problems in membrane structures with rigid and cable boundaries. Inf. Constr. 63,(524), 49–57 (2011)CrossRef
4.
Viglialoro, G., Murcia, J.: A singular elliptic problem related to the membrane equilibrium equations. Int. J. Comput. Math. 90(10), 2185–2196 (2013)MATHCrossRef
5.
Viglialoro, G., Murcia, J., Martínez, F.: Equilibrium problems in membrane structures with rigid boundaries. Inf. Constr. 61(516), 57–66 (2009)CrossRef
Metadata
Title
A Free Boundary Approach to Solve the Equilibrium Equations of a Membrane
Authors
Giuseppe Viglialoro
Álvaro González
Juan Murcia
Copyright Year
2015
Book
Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Print ISBN: 978-3-319-12306-6

Electronic ISBN: 978-3-319-12307-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12307-3_68

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